Question: Simplify the following expression: $\dfrac{36q^5}{66q^4}$ You can assume $q \neq 0$.
$ \dfrac{36q^5}{66q^4} = \dfrac{36}{66} \cdot \dfrac{q^5}{q^4} $ To simplify $\frac{36}{66}$ , find the greatest common factor (GCD) of $36$ and $66$ $36 = 2 \cdot 2 \cdot 3 \cdot 3$ $66 = 2 \cdot 3 \cdot 11$ $ \mbox{GCD}(36, 66) = 2 \cdot 3 = 6 $ $ \dfrac{36}{66} \cdot \dfrac{q^5}{q^4} = \dfrac{6 \cdot 6}{6 \cdot 11} \cdot \dfrac{q^5}{q^4} $ $\phantom{ \dfrac{36}{66} \cdot \dfrac{5}{4}} = \dfrac{6}{11} \cdot \dfrac{q^5}{q^4} $ $ \dfrac{q^5}{q^4} = \dfrac{q \cdot q \cdot q \cdot q \cdot q}{q \cdot q \cdot q \cdot q} = q $ $ \dfrac{6}{11} \cdot q = \dfrac{6q}{11} $